where \({\Gamma _{\bf kq}}\)  is the transition rate from the state with the wave vector \(\bf k\)  to the state with the wave vector \(\bf q\) .
The thermalization rates \({\Gamma _{\bf kq}}\)  obey the Kubo–Martin–Schwinger relation \({\Gamma _{\bf kq}}/{\Gamma _{\bf qk}} = \exp \left( {\left( {{\omega _{\bf k}} - {\omega _{\bf q}}} \right)/T} \right)\) , where \(T\)  is the temperature of intermolecular vibrations of the organic dyes or the temperature of the phonons in the semiconductors [1]}.
Hereafter, we assume the Boltzmann constant to be equal to unity.
